Sequential and Simultaneous Model Predictive Control of a Drainage Canal Network Using an Implicit Diffusive Wave Model

Abstract

Model predictive control (MPC) is an efficient approach to regulate water systems, for both water quantity and quality. It generates optimal control trajectories based on model predictions over a finite horizon. In this research, the focus is on nonlinear MPC with a nonlinear internal model and the comparison of a sequential and simultaneous optimization setup, referred to as sequential and simultaneous nonlinear model predictive control (SeNMPC, SiNMPC), for the solution of the optimum control problem. The representation of the water system in the internal model is based on the diffusive wave model. The model is integrated in time by an unconditionally stable Backward Euler scheme to avoid model instabilities and time step restrictions. This numerical robustness is essential in real-time control applications where large control time steps should not be jeopardized by local grid refinements owing to the system topology. In order to speed up the optimization, an adjoint model is set up to calculate analytical derivatives of the objective function with respect to the optimization variables. Both SeNMPC and SiNMPC are successfully tested on a drainage canal network to regulate water levels and lead to identical results. The SiNMPC shows some advantages over the SeNMPC approach in terms of a higher computational performance and easier options to constrain the optimum control problem.